Approximation of Generalized Schur Complements (Ladder Network)
Butler, Charles Allen
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https://hdl.handle.net/2142/71247
Description
Title
Approximation of Generalized Schur Complements (Ladder Network)
Author(s)
Butler, Charles Allen
Issue Date
1987
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Abstract
The Schur complement of a linear operator on a finite dimensional Hilbert space is discussed and six generalizations are presented. Conditions are established under which these generalizations are equivalent. The infinite dimensional case is then considered and counterexamples are given to show that not all the generalizations extend in a natural way. An approximating sequence is shown to exist for the Schur complement matrix equation. The sequences which work as approximating sequences are classified. Finally, an application to infinite ladder networks of operators is given.
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